Short circuits in power systems a practical guide to IEC 60909 0 ( TQL)

5 Network Types for the Calculation of Short-CircuitCurrents 39 6 Systems up to 1 kV 47 6.1.1 Description of the System is Carried Out by Two Letters 48 6.2 Calculation of Fault Currents

Short Circuits in Power Systems

A Practical Guide to IEC 60909-0

Ismail Kasikci

Second Edition

Cover credit Siemens

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Contents

Preface xi

Acknowledgments xiii

1 Definitions: Methods of Calculations 1

1.1 Time Behavior of the Short-Circuit Current 2

1.2 Short-Circuit Path in the Positive-Sequence System 3

1.3 Classification of Short-Circuit Types 5

1.4 Methods of Short-Circuit Calculation 7

1.4.2 Equivalent Voltage Source 10

1.4.3 Transient Calculation 11

1.4.4 Calculating with Reference Variables 12

1.4.4.1 The Per-Unit Analysis 12

1.4.5.1 Characteristics of the Short-Circuit Current 14

1.4.5.2 Calculation of Switching Processes 14

1.4.5.3 Calculation with pu System 14

1.4.5.4 Calculation with pu Magnitudes 16

1.4.5.5 Calculation with pu System for an Industrial System 17

1.4.5.6 Calculation with MVA System 19

2 Fault Current Analysis 23

3 The Significance of IEC 60909-0 29

4 Supply Networks 33

4.1 Calculation Variables for Supply Networks 34

4.2 Lines Supplied from a Single Source 35

5 Network Types for the Calculation of Short-Circuit

Currents 39

6 Systems up to 1 kV 47

6.1.1 Description of the System is Carried Out by Two Letters 48

6.2 Calculation of Fault Currents 49

6.2.1 System Power Supplied from Generators: 50

6.3.1 Description of the System 52

6.4.1 Description of the System 53

6.5 Transformation of the Network Types Described to Equivalent

Circuit Diagrams 54

6.6.1 Example 1: Automatic Disconnection for a TN System 56

6.6.1.1 Calculation for a Receptacle 56

6.6.1.2 For the Heater 56

6.6.2 Example 2: Automatic Disconnection for a TT System 57

7 Neutral Point Treatment in Three-Phase Networks 59

7.1 Networks with Isolated Free Neutral Point 63

7.3 Networks with Low-Impedance Neutral Point Treatment 66

8 Impedances of Three-Phase Operational Equipment 71

8.1 Network Feed-Ins, Primary Service Feeder 71

8.5 Short-Circuit Current-Limiting Choke Coils 96

8.7 Consideration of Capacitors and Nonrotating Loads 98

8.9.1 Wind Power Plant with AG 100

8.9.2 Wind Power Plant with a Doubly Fed Asynchronous Generator 101

Contents vii

8.9.3 Wind Power with Full Converter 101

8.10 Short-Circuit Calculation on Ship and Offshore Installations 102

8.11.1 Example 1: Calculate the Impedance 104

8.11.2 Example 2: Calculation of a Transformer 104

8.11.3 Example 3: Calculation of a Cable 105

8.11.4 Example 4: Calculation of a Generator 105

8.11.5 Example 5: Calculation of a Motor 106

8.11.6 Example 6: Calculation of an LV motor 106

8.11.7 Example 7: Design and Calculation of a Wind Farm 106

8.11.7.1 Description of the Wind Farm 106

8.11.7.2 Calculations of Impedances 111

8.11.7.3 Backup Protection and Protection Equipment 116

8.11.7.4 Thermal Stress of Cables 118

8.11.7.5 Neutral Point Connection 119

8.11.7.6 Neutral Point Transformer (NPT) 119

8.11.7.7 Network with Current-Limiting Resistor 120

8.11.7.8 Compensated Network 124

8.11.7.9 Insulated Network 125

8.11.7.10 Grounding System 125

9 Impedance Corrections 127

9.1 Correction Factor KGfor Generators 128

9.2 Correction Factor KKWfor Power Plant Block 129

9.3 Correction Factor KTfor Transformers with Two and Three

10 Power System Analysis 133

10.2 Fundamentals of Symmetrical Components 137

10.2.1 Derivation of the Transformation Equations 139

10.3 General Description of the Calculation Method 140

11 Calculation of Short-Circuit Currents 147

11.1 Three-Phase Short Circuits 147

11.2 Two-Phase Short Circuits with Contact to Ground 148

11.3 Two-Phase Short Circuit Without Contact to Ground 149

11.4 Single-Phase Short Circuits to Ground 150

11.5 Peak Short-Circuit Current, ip 153

11.6 Symmetrical Breaking Current, Ia 155

11.7 Steady-State Short-Circuit Current, Ik 157

12 Motors in Electrical Networks 161

12.1 Short Circuits at the Terminals of Asynchronous Motors 161

12.2 Motor Groups Supplied from Transformers with Two Windings 163

12.3 Motor Groups Supplied from Transformers with Different Nominal

Voltages 163

13 Mechanical and Thermal Short-Circuit Strength 167

13.1 Mechanical Short-Circuit Current Strength 167

13.2 Thermal Short-Circuit Current Strength 173

13.3 Limitation of Short-Circuit Currents 176

13.4 Examples for Thermal Stress 176

13.4.1 Feeder of a Transformer 176

13.4.2 Mechanical Short-Circuit Strength 178

14 Calculations for Short-Circuit Strength 185

14.1 Short-Circuit Strength for Medium-Voltage Switchgear 185

14.2 Short-Circuit Strength for Low-Voltage Switchgear 186

15 Equipment for Overcurrent Protection 189

16 Short-Circuit Currents in DC Systems 199

16.1 Resistances of Line Sections 201

17 Power Flow Analysis 207

17.1 Systems of Linear Equations 208

17.3.5 Calculation of Node Voltages at Predetermined Node Power 215

17.3.6 Calculation of Power Flow 215

17.3.6.1 Type of Nodes 216

17.3.6.2 Type of Loads and Complex Power 216

17.3.7 Linear Load Flow Equations 218

17.3.8 Load Flow Calculation by Newton–Raphson 219

17.3.9 Current Iteration 223

17.3.9.1 Jacobian Method 223

17.3.10 Gauss–Seidel Method 224

17.3.12 Power Flow Analysis in Low-Voltage Power Systems 226

17.3.13 Equivalent Circuits for Power Flow Calculations 227

17.3.14.1 Calculation of Reactive Power 228

17.3.14.2 Application of Newton Method 228

17.3.14.3 Linear Equations 229

17.3.14.4 Application of Cramer’s Rule 229

17.3.14.5 Power Flow Calculation with NEPLAN 230

Contents ix

18 Examples: Calculation of Short-Circuit Currents 233

18.1 Example 1: Radial Network 233

18.2 Example 2: Proof of Protective Measures 235

18.3 Example 3: Connection Box to Service Panel 237

18.4 Example 4: Transformers in Parallel 238

18.5 Example 5: Connection of a Motor 240

18.6 Example 6: Calculation for a Load Circuit 241

18.7 Example 7: Calculation for an Industrial System 243

18.8 Example 8: Calculation of Three-Pole Short-Circuit Current and Peak

Short-Circuit Current 244

18.10 Example 10: Supply to a Factory 249

18.11 Example 11: Calculation with Impedance Corrections 250

18.12 Example 12: Connection of a Transformer Through an External

Network and a Generator 253

18.13 Example 13: Motors in Parallel and their Contributions to the

Short-Circuit Current 255

18.14 Example 14: Proof of the Stability of Low-Voltage Systems 257

18.15 Example 15: Proof of the Stability of Medium-Voltage and

Secondary Symbols, Upper Right, Left 287

American Cable Assembly (AWG) 287

Index 289

This book is the result of many years of professional activity in the area of powersupply, teaching at the VDE, as well as at the Technical Academy in Esslingen.Every planner of electrical systems is obligated today to calculate the single-pole

or three-pole short-circuit current before and after the project managementphase IEC 60909-0 is internationally recognized and used This standard will

be discussed in this book on the basis of fundamental principles and technical

references, thus permitting a summary of the standard in the simplest and most

understandableway possible The rapid development in all areas of technology isalso reflected in the improvement and elaboration of the regulations, in particu-lar in regard to IEC 60909-0 Every system installed must not only be suitable fornormal operation, but must also be designed in consideration of fault conditionsand must remain undamaged following operation under normal conditions andalso following a fault condition Electrical systems must therefore be designed

so that neither persons nor equipment are endangered The dimensioning, costeffectiveness, and safety of these systems depend to a great extent on being able

to control short-circuit currents With increasing power of the installation, theimportance of calculating short-circuit currents has also increased accordingly.Short-circuit current calculation is a prerequisite for the correct dimensioning ofoperational electrical equipment, controlling protective measures and stabilityagainst short circuits in the selection of equipment Solutions to the problems

of selectivity, back-up protection, protective equipment, and voltage drops inelectrical systems will not be dealt with in this book The reduction factors, such

as frequency, temperatures other than the normal operating temperature, type

of wiring, and the resulting current carrying capacity of conductors and cableswill also not be dealt with here

This book comprises the following sections:

Chapter 1 describes the most important terms and definitions, together withrelevant processes and types of short circuits

Chapter 2 is an overview of the fault current analysis

Chapter 3 explains the significance, purpose, and creation of IEC 60909-0.Chapter 4 deals with the network design of supply networks

Chapter 5 gives an overview of the network types for low, medium and voltage network

high-Chapter 6 describes the systems (network types) in the low-voltage network(IEC 60364) with the cut-off conditions

is not possible in the positive-sequence system The method of symmetrical ponents is therefore described here.

com-Chapter 11 is devoted to the calculation of short-circuit types

Chapter 12 discusses the contribution of high-voltage and low-voltage motors

to the short-circuit current

Chapter 13 deals with the subject of mechanical and thermal stresses in ational equipment as a result of short-circuit currents

oper-Chapter 14 gives an overview of the design values for short-circuit currentstrength

Chapter 15 is devoted to the most important overcurrent protection devices,with time–current characteristics

Chapter 16 gives a brief overview of the procedure for calculating short-circuitcurrents in DC systems

Chapter 17 gives an introduction into power flow analysis

Chapter 18 represents a large number of examples taken from practice whichenhance the understanding of the theoretical foundations A large number ofdiagrams and tables that are required for the calculation simplify the applica-tion of the IEC 60909 standard as well as the calculation of short-circuit currentsand therefore shorten the time necessary to carry out the planning of electricalsystems

I am especially indebted to Dr.-Ing Waltraud Wüst, Dr Martin Preuss fromWiley-VCH and Kishore Sivakolundu from SPI for critically reviewing themanuscript and for valuable suggestions

At this point, I would also like to express my gratitude to all those colleagueswho supported me with their ideas, criticism, suggestions, and corrections Myheartiest appreciation is due to Wiley Press for the excellent cooperation and theirsupport in the publication of this book

Furthermore, I welcome every suggestion, criticism, and idea regarding the use

of this book from those who read the book

Finally, without the support of my family this book could never have been ten In recognition of all the weekends and evenings I sat at the computer, I ded-icate this book to my family

writ-Weinheim

21.07.2017

Ismail Kasikci

I would like to thank the companies Siemens and ABB for their help with figures,pictures, and technical documentation In particular, as a member, I am alsoindebted to the VDE (Association for Electrical, Electronic and InformationTechnologies) for their support and release of different kinds of tables and data.Additionally, I would like to thank Wiley for publishing this book and espe-cially Dr.-Ing Waltraud Wüst, Dr Martin Preuss from Wiley-VCH and KishoreSivakolundu from SPI for their assistance in supporting me and checking thebook for clarity

Finally, I appreciate the designers and planners for their feedbacks, the studentsfor their useful recommendations, and the critics

1

Definitions: Methods of Calculations

The following terms and definitions correspond largely to those defined in IEC60909-0 Refer to this standard for all the terms not used in this book

The terms short circuit and ground fault describe faults in the isolation of

oper-ational equipment, which occur when live parts are shunted out as a result

1) Causes:

• Overtemperatures due to excessively high overcurrents;

• Disruptive discharges due to overvoltages; and

• Arcing due to moisture together with impure air, especially on insulators

2) Effects:

• Interruption of power supply;

• Destruction of system components; and

• Development of unacceptable mechanical and thermal stresses in cal operational equipment

electri-3) Short circuit: According to IEC 60909-0, a short circuit is the accidental or

intentional conductive connection through a relatively low resistance orimpedance between two or more points of a circuit that are normally atdifferent potentials

4) Short-circuit current: According to IEC 60909-0, a short-circuit current

results from a short circuit in an electrical network

It is necessary to differentiate between the short-circuit current at the tion of the short circuit and the transferred short-circuit currents in the net-work branches

posi-5) Initial symmetrical short-circuit current: The effective value of the

symmet-rical short-circuit current at the moment at which the short circuit arises,when the short-circuit impedance has its value from the time zero

6) Initial symmetrical short-circuit apparent power: The short-circuit power

represents a fictitious parameter During the planning of networks, theshort-circuit power is a suitable characteristic number

Short Circuits in Power Systems: A Practical Guide to IEC 60909-0,Second Edition Ismail Kasikci.

© 2018 Wiley-VCH Verlag GmbH & Co KGaA Published 2018 by Wiley-VCH Verlag GmbH & Co KGaA.

7) Peak short-circuit current: The largest possible momentary value of the short

circuit occurring

8) Steady-state short-circuit current: Effective value of the initial symmetrical

short-circuit current remaining after the decay of all transient phenomena

9) Direct current (d.c.) aperiodic component: Average value of the upper and

lower envelope curve of the short-circuit current, which slowly decays

to zero

10) Symmetrical breaking current: The effective value of the short-circuit

cur-rent that flows through the contact switch at the time of the first contactseparation

11) Equivalent voltage source: The voltage at the position of the short circuit,

which is transferred to the positive-sequence system as the only effectivevoltage and is used for the calculation of the short-circuit currents

12) Superposition method: Considers the previous load of the network before the

occurrence of the short circuit It is necessary to know the load flow and thesetting of the transformer step switch

13) Voltage factor: Ratio between the equivalent voltage source and the network voltage, Un, divided by√

3

14) Equivalent electrical circuit: Model for the description of the network by an

equivalent circuit

15) Far-from-generator short circuit: The value of the symmetrical alternating

current (a.c.) periodic component remains essentially constant

16) Near-to-generator short circuit: The value of the symmetrical a.c periodic

component does not remain constant The synchronous machine first ers an initial symmetrical short-circuit current, which is more than twice therated current of the synchronous machine

deliv-17) Positive-sequence short-circuit impedance: The impedance of the

positive-sequence system as seen from the position of the short circuit

18) Negative-sequence short-circuit impedance: The impedance of the

negative-sequence system as seen from the position of the short circuit

19) Zero-sequence short-circuit impedance: The impedance of the zero-sequence

system as seen from the position of the short circuit Three times the value

of the neutral point to ground impedance occurs

20) Short-circuit impedance: Impedance required for the calculation of the

short-circuit currents at the position of the short circuit

1.1 Time Behavior of the Short-Circuit Current

Figure 1.1 shows the time behavior of the short-circuit current for the occurrence

of far-from-generator and near-to-generator short circuits

The d.c aperiodic component depends on the point in time at which the shortcircuit occurs For a near-to-generator short circuit, the subtransient and thetransient behaviors of the synchronous machines are important Following thedecay of all transient phenomena, the steady state sets in

1.2 Short-Circuit Path in the Positive-Sequence System 3

d.c component id.c.of the short-circuit current

d.c component id.c.of the short-circuit current

Figure 1.1 Time behavior of the short-circuit current (see Ref [1]) (a) Far-from-generator short

circuit and (b) near-to-generator short circuit I′′

k: initial symmetrical short-circuit current; ip:

peak short-circuit current; id.c.: decaying d.c aperiodic component; and A: initial value of d.c.

aperiodic component.

1.2 Short-Circuit Path in the Positive-Sequence System

For the same external conductor voltages, a three-phase short circuit allowsthree currents of the same magnitude to develop among the three conductors.Therefore, it is only necessary to consider one conductor in further calculations.Depending on the distance from the position of the short circuit from thegenerator, it is necessary to consider near-to-generator and far-from-generatorshort circuits separately For far-from-generator and near-to-generator shortcircuits, the short-circuit path can be represented by a mesh diagram with an

a.c voltage source, reactances X, and resistances R (Figure 1.2) Here, X and R

replace all components such as cables, conductors, transformers, generators,and motors

Figure 1.2 Equivalent circuit of the

short-circuit current path in the positive-sequence system.

The following differential equation can be used to describe the short-circuitprocess:

ik⋅ Rk+Lkdik

where𝜓 is the phase angle at the point in time of the short circuit The

inho-mogeneous first-order differential equation can be solved by determining the

homogeneous solution ikand a particular solution I′′

𝜑k=𝜓 − 𝜈 = arctan X

Figure 1.3 shows the switching processes of the short circuit

For the far-from-generator short circuit, the short-circuit current is, therefore,made up of a constant a.c periodic component and the decaying d.c aperiodiccomponent From the simplified calculations, we can now reach the followingconclusions:

1) The short-circuit current always has a decaying d.c aperiodic component inaddition to the stationary a.c periodic component

2) The magnitude of the short-circuit current depends on the operating angle ofthe current It reaches a maximum at𝛾 = 90∘ (purely inductive load) This case

serves as the basis for further calculations

3) The short-circuit current is always inductive

1.3 Classification of Short-Circuit Types 5

Figure 1.3 Switching processes of the short circuit.

1.3 Classification of Short-Circuit Types

For a three-phase short circuit, three voltages at the position of the short circuitare zero The conductors are loaded symmetrically Therefore, it is sufficient

to calculate only in the positive-sequence system The two-phase short-circuitcurrent is less than that of the three-phase short circuit, but largely close tosynchronous machines The single-phase short-circuit current occurs mostfrequently in low-voltage (LV) networks with solid grounding The doubleground connection occurs in networks with a free neutral point or with a groundfault neutralizer grounded system

For the calculation of short-circuit currents, it is necessary to differentiatebetween the far-from-generator and the near-to-generator cases

1) Far-from-generator short circuit

When double the rated current is not exceeded in any machine, we speak of afar-from-generator short circuit

2) Near-to-generator short circuit

When the value of the initial symmetrical short-circuit current I′′

k exceedsdouble the rated current in at least one synchronous or asynchronous machine

at the time the short circuit occurs, we speak of a near-to-generator shortcircuit

1) Three-phase short circuits:

• connection of all conductors with or without simultaneous contact toground;

• symmetrical loading of the three external conductors;

• calculation only according to single phase

2) Two-phase short circuits:

• unsymmetrical loading;

• all voltages are nonzero;

• coupling between external conductors;

• for a near-to-generator short circuit I′′

k2> I′′

k3

3) Single-phase short circuits between phase and PE:

• very frequent occurrence in LV networks

4) Single-phase short circuits between phase and N:

• very frequent occurrence in LV networks

5) Two-phase short circuits with ground:

• in networks with an insulated neutral point or with a suppression coil

in conductors and earth return

L3 L2 L1

L3 L2 L1

I″k1I″kE2E

Figure 1.4 Types of short-circuit currents in three-phase networks [1].

1.4 Methods of Short-Circuit Calculation 7

With a suppression coil grounded system, a residual ground fault current IRestoccurs ICand IRestare special cases of I′′

k

1.4 Methods of Short-Circuit Calculation

The measurement or calculation of short-circuit current in LV networks on finalcircuits is very simple In meshed and extensive power plants, the calculation ismore difficult because of the short-circuit current of several partial short-circuitcurrents in conductors and earth return

The short-circuit currents in three-phase systems can be determined by threedifferent calculation procedures:

1) superposition method for a defined load flow case;

2) calculating with the equivalent voltage sourcec√⋅Un

3 at the fault location; and3) transient calculation

1.4.1 Superposition Method

The superposition method is an exact method for the calculation of the circuit currents The method consists of three steps The voltage ratios andthe loading condition of the network must be known before the occurrence ofthe short circuit In the first step, the currents, voltages, and internal voltagesfor steady-state operation before onset of the short circuit are calculated(Figure 1.5b) The calculation considers the impedances, power supply feeders,and node loads of the active elements In the second step, the voltage applied tothe fault location before the occurrence of the short circuit and the current dis-tribution at the fault location are determined with a negative sign (Figure 1.5b).This is the only voltage source in the network The internal voltages are short-circuited In the third step, both the conditions are superimposed We thenobtain a zero voltage at the fault location The superposition of the currents alsoleads to the value zero The disadvantage of this method is that the steady-statecondition must be specified The data for the network (effective and reactivepower, node voltages, and the step settings of the transformers) are oftendifficult to determine The question also arises: Which operating state leads tothe greatest short-circuit current?

short-The superposition method assumes that the power flow is known of the work before the fault inception and the setting of the tap changer of the trans-former and the voltage set points of the generators

net-By the superposition method, the power state is superimposed with an ments state before the short circuit occurs For this condition, the consideration

amend-of positive sequence is sufficient

The network consists of i = 1,…,n load nodes and j = 1,…,m generators and

power supply applications With a suitable program, the load flow can be culated for a network condition After the changes in the network through theshort circuit, there are other values at each node For a three-phase short circuit,the voltage at the fault point equals zero This condition is also fulfilled when the

cal-1 F

n

G

3~

1 F

n

~

.

.

.

.

(d)

(a)

~

1 F

.

.

1.4 Methods of Short-Circuit Calculation 9

same voltage is given at the fault location but with an opposite voltage sign Allnetwork feeders, synchronous, and asynchronous machines are replaced by theirinternal impedances (Figure 1.5d)

The calculation of a short-circuit current is a linear problem that can be solvedeasily with linear equations There is a linear relationship between the node volt-ages and node currents

With the help of nodal admittance matrix systems, linear equations can besolved All impedances are converted to the LV side of the transformers In con-trast to the load flow calculation, an iteration is not required The equations are

obtained at the short-circuit location i in matrix notation.

Since the operating voltage U(1)f = Un√

3is not known at the fault location, for theequivalent voltage source at the fault point can be introduced

−U(1)f = c ⋅ Un

√3

(1.17)

At the short-circuit point, the only active voltage is the Thevenin equivalentvoltage source of the system

1.4.2 Equivalent Voltage Source

Figure 1.6 shows an example of the equivalent voltage source at the short-circuitlocation F as the only active voltage of the system fed by a transformer with

or without an on-load tap changer All other active voltages in the systemare short-circuited Thus, the network feeder is represented by its internal

impedance, ZQt, transferred to the LV side of the transformer and the former by its impedance referred to the LV side The shunt admittances of the line,the transformer, and the nonrotating loads are not considered The impedances

trans-of the network feeder and the transformer are converted to the LV side

The transformer is corrected with KT, which will be explained later

The voltage factor c (Table 1.1) will be described briefly as follows:

If there are no national standards, it seems adequate to choose a voltage

fac-tor c, according to Table 1.1, considering that the highest voltage in a normal

Figure 1.6 Network circuit with equivalent voltage source [2] (a) System diagram and

(b) equivalent circuit diagram of the positive-sequence system.

1.4 Methods of Short-Circuit Calculation 11

Table 1.1 Voltage factor c, according to IEC 60909-0: 2016-10 [1].

Nominal voltage, Un Voltage factor c for calculation of

0.95 b) 0.9 c) High voltage d)

>1–35 kV

(IEC 38, Tables III and IV)

a) cmaxUnshould not exceed the highest voltage Umfor equipment of power systems.

b) For LV systems with a tolerance of ±6%, for example, systems renamed from 380 to

400 V.

c) For LV systems with a tolerance of ±10%.

d) If no nominal voltage is defined, cmaxUn=Umor cminUn=0.90 Umshould be applied.

(undisturbed) system does not differ, on average, by more than approximately+5% (some LV systems) or +10% (some high-voltage, HV, systems) from the nom-

inal system voltage Un[3]

1) The different voltage values depending on time and position

2) The step changes of the transformer switch

3) The loads and capacitances in the calculation of the equivalent voltage sourcecan be neglected

4) The subtransient behavior of generators and motors must be considered

This method assumes the following conditions:

1) The passive loads and conductor capacitances can be neglected

2) The step setting of the transformers need not be considered

3) The excitation of the generators need not be considered

4) The time and position dependence of the previous load (loading state) of thenetwork need not be considered

1.4.3 Transient Calculation

With the transient method, the individual operating equipment and, as a result,the entire network are represented by a system of differential equations Thecalculation is very tedious The method with the equivalent voltage source is asimplification relative to the other methods Since 1988, it has been standard-ized internationally in IEC 60909-0 The calculation is independent of a currentoperational state Therefore, in this book, the method with the equivalent voltagesource will be dealt with and discussed

1.4.4 Calculating with Reference Variables

There are several methods for performing short-circuit calculations with lute and reference impedance values A few methods are summarized here, andexamples are calculated for comparison To define the relative values, there aretwo possible reference variables

abso-For the characterization of electrotechnical relationships, we require the fourparameters:

1) voltage U in V;

2) current I in A;

3) impedance Z in Ω; and

4) apparent power S in VA.

Three methods can be used to calculate the short-circuit current:

1) The Ohm system: units – kV, kA, V, and MVA

2) The per-unit (pu) system: this method is used predominantly for electrical machines; all four parameters u, i, z, and s are given as per unit (unit = 1) The

reference value is 100 MVA The two reference variables for this system are

UB and SB Example: The reactances of a synchronous machine Xd, X′

d, and

X′′

d are given in pu or in %pu, multiplied by 100%

3) The %/MVA system: this system is especially well suited for the quick mination of short-circuit impedances As a formal unit, only the % symbol isadded

Today, the power system consists of complex and complicated mesh, ring, andradial networks with many transformers, generators, and cables The calcula-tion of such a circuit can be very tedious and incorrect The use of sophisticatedcomputer programs is a big help for engineers On the other hand, for a quickcalculation a simple method, per unit system also can be used However, thismethod is not accepted worldwide and is not standardized by IEC, EN, or IEEEcommittees

The pu method uses the electrical variables U , I, Z, and S They are based on a

dimensionless same references, namely, Ubase, Ibase, Zbase, or Sbase The resulting

dimensionless quantities are described with the lowercase u , i, z, or s.

A pu system is defined as follows:

Per unit value (pu) = the actual value (in any unit)

the base or reference value (in the same unit)

Sbase

Ibase= Sbase

U

1.4 Methods of Short-Circuit Calculation 13

Only a single global base value is selected in the short-circuit currentcalculation This reference value is then used for all other networks The choice

of reference values can be carried out arbitrarily in principle However, it isappropriate to select the rated voltage at the short-circuit location as a referencevoltage For example, as reference apparent power is the rated apparent power

of the largest transformer in the network or a power of the same selectedmagnitude (e.g., 100 MVA) The best choice of base can be achieved when theimpedances and currents in easily handled orders of magnitude

It should be noted that related parameters’ individual resources, such as the

rel-ative short-circuit voltage of a transformer ukror related subtransient reactance

x′′

d of the generator, are always relative to a base, which consists of the designparameters of the particular equipment In a short-circuit current calculation asper pu method, these parameters must first be converted to the selected globalbasis If we give an example for voltage and current, the expression is as follows:

Upu= Uactual

Ubase

Ipu= Iactual

Ibase

Note that the voltage according to the international system of units (SI) is not

V , but U The letter V is a unit in this case V is used especially in Anglo-Saxon

Remember that a symmetrical three-phase system has two voltages, line–line

voltage UL(Un) and ULN(U0) By definition:

ULN = √UL

3Now consider:

ULbase∕√

3

ULbase =ULpu

Consider that the factor√

3 disappears in the pu equation

1.4.4.2 The %/MVA Method

The %/MVA method can be considered as a modification of the pu method anddesigned specifically for the HV network calculation The impedances of theelectrical equipment can be determined easily in %/MVA from the synchronousmachine and transformer characteristics It utilizes the fact that for the pu

calculation, apparent power Sbaseis completely arbitrary Consequently, instead

of Sbase, the dimensionless value 1 is inserted This has the result that the relatedsizes of the pu are no longer dimensionless

The related impedances can be represented in %/MVA The %/MVA method

has the advantage that a conversion with t2 or 1/t2 eliminates the tion of impedances in the voltage level on the transformers Furthermore, allimpedances of resources and the dimensioning data can be obtained from thenameplate

The short-circuit current is composed of two parts The first term describes thea.c (continuous current) and the second term the compensation process

ik(t)= ̂ ik⋅ sin(𝜔t − Ψ + 𝜑u) − ̂ ik⋅ sin(Ψ − 𝜑) ⋅ e−(t∕𝜏)

The size of the short-circuit current is therefore dependent on the phase angle

𝜑 = arc tan X

R, the time constant𝜏 = L

R , the time t, and the switching angle Ψ.

Thus we can obtain many shifts by changing the sizes (Figure 1.7)

Given are the following sizes of short-circuit current (Figure 1.8):

RQ

XQ =0.176, 𝜑 = −80∘, 𝜑u= −170∘, 𝜏 = 0.018 ms,

3⋅ 𝜏 = 0.054ms, 𝜅 = 1.597

Draw the switching process of the short circuit

Given is a system with 20/6 kV network (Figure 1.9)

1.4 Methods of Short-Circuit Calculation 15

Network 2000 MVA

20 kV

6 kV T

Q

Motor 3 + 4

M 3~

M 3~

Given: UB=Un=6 kV bzw 20 kV, SB=100 MVA Calculate example 1.4.5.3using pu magnitude

1.4 Methods of Short-Circuit Calculation 17

Impedances of motors in pu systems:

PrM ⋅ SB

U2

B,6 kV

= 12

Given is Figure 1.10 Calculate the short circuit power and short-circuit currents

of an industrial power plant with the pu method

First, the equivalent circuit diagram is drawn (Figure 1.11)

154.5 kV

Q

31.5 kV

1600 kVA 6%

50 MVA 11.94%

Impedance of the power supply:

On distribution transformer:

I′′=Ipu⋅ IB=3.8 pu⋅ 1835A = 6.973kA

1.4 Methods of Short-Circuit Calculation 19

Short-circuit power on the primary side of the transformer:

I′′

k(0.4 kV)=Ipu⋅ IB=0.24924 pu⋅ 1.835kA = 0.457kA

Figure 1.12 shows a power plant with auxiliary power system and power ply Calculate using the %/MVA system at the busbar SS circuit power, the peakshort-circuit current and the breaking current

sup-The total reactance at the fault is calculated with the aid of the equivalent circuitshown in Figure 1.13 by gradual power conversion

1) Calculation of the reactance of the individual resources

93.7 MVA 11.5%

8 MVA 7%

M 3~

2) Parts of each feed on the short-circuit power.

With the total reactance, we can determine the circuit power

1.4 Methods of Short-Circuit Calculation 21

Part of each motor gives:

Part of the generator:

From Figure 13.3, we get the𝜇 factors for tv=0.1 s

For each motor:

S′′

kM1

SrM1 =

14.82.69=5.50⇒ 𝜇 = 0.77

For motor groups:

For each motor:

5) Determination of the individual feeds to the switching capacity

For each motor:

SaM1=𝜇 ⋅ q ⋅ S′′

kM1=0.77⋅ 0.55 ⋅ 14.8MVA = 6.3MVA

For motor groups:

SaM2=𝜇 ⋅ q ⋅ S′′ =0.76⋅ 0.3 ⋅ 20.3MVA = 64.6MVA

For the generator:

Initial short-circuit a.c.:

2

Fault Current Analysis

Every electrical engineer and designer is committed to perform before and afterthe project is constructed, especially the calculation of the single- or three-phaseshort-circuit current in electric power systems to check the protection andshort-circuit strength of the electrical systems for the selection of equipmentand to adjust the protective devices

This book deals with the calculation of short circuits in electrical installationsand the load flow in low-voltage and high-voltage networks to the highest indus-try standards and regulations (IEC 60909-0) The purpose of the review of funda-mentals of power systems and short-circuit calculation by using the standards is

to obtain a better understanding of the basic complexities involved in a.c systems.The presentation of the regulation is maintained and summarized in a simpleand understandable way, so that the reader can do his or her job without muchtrouble

Each electrical system must be designed not only for the normal operation, butalso for abnormal conditions such as short circuits Therefore, electrical systemsare to be dimensioned, so that neither people nor property values are jeopardized.The design for economy and safety is strongly dependent on the calculation ofshort circuits

The knowledge of the magnitude of the short-circuit currents occurring is adecisive factor in the design and selection of system components in electricalpower grids The three-phase short-circuit currents cause a few exceptions tothe strongest mechanical and thermal stresses of the equipment

The initial short-circuit current of the three-phase short circuit, I′′

k3, is thecentral value of any other relevant information for the design characteristicshort-circuit current All other short circuits can be calculated based on thestandardized factors

For the calculation of the initial short-circuit a.c in three-phase power systems,there is an exact calculation using the superposition method and the other stan-dardized method according to IEC 60909-0, the equivalent voltage source to theshort circuit at the fault location in the system

It is assumed that there is always a perfect short circuit in both the calculationmethods (e.g., no arcing or contact resistances provided)

Short Circuits in Power Systems: A Practical Guide to IEC 60909-0,Second Edition Ismail Kasikci.

© 2018 Wiley-VCH Verlag GmbH & Co KGaA Published 2018 by Wiley-VCH Verlag GmbH & Co KGaA.

According to IEC 60909-0, the standardized short-circuit calculation is avery simple method, which has the advantage of minimum data and equipmentparameters to get sufficiently precise results.

The method calculates the maximum and minimum short-circuit currents,irrespective of the load flow condition based on standardized correction factorsfor generators and transformers On the other hand, the superposition methodrequires the complete data of the system

The load flow, the voltages at all the feeds, the transformer tap positions, theconsumer loads, and so on, must be taken into consideration However, all ofthese do not necessarily lead to the maximum short-circuit current

For the calculation of the short-circuit current, the voltage at the short-circuitnode before the occurrence of a short circuit is required By replacing this valuewith an equivalent voltage source, the short-circuit current can be determinedapproximately without taking into account the power flow calculation only withthe condition of reverse feed

A reasonable assumption for the voltage source in the “reverse feed” gives theequivalent voltage at the short-circuit location,c√⋅Un

3, where c is the voltage factor and Unis the network nominal system voltage The equivalent voltage source isthe only active voltage of the system All network feeders and synchronous andasynchronous motors are replaced by their internal impedances Whereas the

network’s generators are simplified or replaced by their subtransient X′′

d that can

be found or obtained from the data sheet of the generators

Wind turbines with a full converter (a full-scale power converter) are limited

to the rated current and do not contribute, or only marginally contribute, to theshort-circuit current According to IEC 60909-0, asynchronous generators are

modeled by the equivalent impedance ZM

The increasing amount of installed capacity in the high-voltage level increasesthe short-circuit power in the networks, whereby higher fault currents arise Eventhe choice of neutral point treatment, as well as the network, forms a massiveinfluence on the protection concept

Networks with isolated neutral or resonant-grounded phase faults in overheadnetworks are usually self-extinguishing The protection relays should not inter-vene in this case, but only when standing shorts, as they occur in cable networks

or overhead line conductors For these special arrangements, earth fault relays orwatt-metric relays are required

Low-impedance grounded systems and single-phase and multiphase shortcircuits are detected by the same electric protective device Each short circuitcauses a high-fault current, which is detectable and switched off selectively bythe protective device Typically, a multiphase reclosure tries to give the chance ofself-healing and, on the other side, the network users are affected by the disorder

If it fails, short interruption is switched off three-phase

For the protection of medium-voltage networks, which are not usually designed

as a mesh system, an independent maximum time overcurrent protection is used

The setting of the overcurrent relay of trip factor k must be known, which links

the breaking current and the current setting For all of these, the short-circuitcurrent calculation is essential

Fault Current Analysis 25

A three-phase system can be temporarily or permanently disturbed by errors,especially short-circuit measures or consumers To calculate, the operatingvariable computational models and algorithms are needed for solving systems

of power generation, transmission, and distribution of a comprehensive tool forplanning, design, analysis, optimization, and management of any network ofenergy supply

Due to the liberalization of energy markets and, in particular, the rapid sion of renewable energy, the demands on the network planning and managementprocesses are becoming increasingly complex Complex network technologiesand network topologies are impossible today without calculation programs

expan-The scope of power calculations and system planning may be as follows:

• balanced and unbalanced load flow calculations in coupled and meshed a.c./d.c systems, including any power plant and network control functions;

• short-circuit current calculation, according to IEC 60909-0, IEEE 41, ANSIC37, G74, and IEC 61363, as well as the complete overlay method taking intoaccount the voltage support of inverters and multiple-error-calculating anyfault;

• fast power failure calculation with the support of parallel computing tures;

struc-• network state estimation (as for supervisory control and data acquisition,SCADA, applications);

• protection coordination and distance protection devices, including protectionsimulation;

• arc fault calculation, according to IEEE 1584-2002 and NFPA 70E-2012;

• calculation of power quality, including harmonic load flow (IEC 61000-3-6);flicker calculation, according to IEC 61400-21 and IEC 61000-4-15; and filtersizing;

• separation points optimization in medium-voltage systems and optimization

of compensation devices;

• optimization of transformer tap changers in directional power flow;

• reliability calculations, including optimal restocking strategies;

• optimal load flow calculation for active and reactive power optimizations mal power flow, OPF);

(opti-• stability calculations (root mean squares (RMS)), which include power plants,consumers, and protection devices;

• calculation of electromagnetic transient (EMT) phenomena (e.g., overvoltagesand ferroresonances by transformer saturation);

• computing eigenvalues, eigenvectors, and participation factors; and

• modeling virtual power plants

Appropriate programs can provide the assessment and selection of cal equipment, the calculation of the mechanical and thermal short-circuitstrengths, the calculation of short-circuit currents, selectivity, and backupprotection for the selection of overcurrent protective devices, as well as thecalculation of the temperature that increases in the control cabinets

electri-Transformers with or without medium voltage, generators, and neutral mainscan supply the networks A neutral power supply can be displayed by setting

the impedances of the loop impedance or short-circuit currents Circuits can beoptionally charged to the hedging of parallel cables through a protective device,

a single hedge parallel cable with several protective devices, and dimensioned.The chosen feeds can be connected to each other through directed or undirectedcouplings Thus, it can be explained by the resulting possibility of defining thevarious required operating modes (e.g., normal operation and emergency opera-tion), represent the main supply practical and be included in the calculation

A parallel network operation can be displayed by combining two nonsimilarfeeds via a nondirectional clutch Feeds on the subdistribution level can also beincluded in the calculation, and a presentation of separate networks is possible

In the case of selecting a transformer with medium voltage, a medium-voltageswitchgear is required and is an important factor to size the transformer’s feederelements

Transformer, generator, or neutral network in feed according to the selection

of feeder types, switchgear to the transformer or generator or neutral networksupply, which consists of a switching device, a circuit breaker, disconnector withfuse, fuse switch disconnectors or fuse with base, cable or busbar connectionwith switching device before the feed point, which stands as a type of the circuitbreaker, a circuit breaker, air circuit breakers, switch disconnectors with fuse, fuseswitch disconnectors or fuse with base to choose from

The distributors are subdistribution, group switch, busway, busway center feed,

or distribution with equivalent impedances for selection Concerning selectingthese elements, there are specific requirements to meet the design again (e.g.,whether the connection line is to be performed as a busbar or as a cable andwhich and how many switching devices are to be used) A cable selection section

is also provided for laying so that the influenced values of the current-carryingcapacity are taken into account in the dimensioning The distributors are alwaysinserted on a busbar in the graphic This can be the busbar, which symbolizes theentry point, the busbar of an already connected distributor, or the representa-tion of a current rail track so that, in this way, the network can be branched as aradial network

Final circuits are available as elements consumers with fixed connection, socketcircuits, motors, loading units, capacitors, and dummy loads as items to choosefrom These, in turn, are connected to the busbar of existing subdistributors or therepresentation of a current rail track, or directly to the entry point symbolizingbusbar There are also various options in the placement of these elements in thenetwork diagram

In practice, a selectivity detection is often required (e.g., the equipment ofemergency power supply) The switching device selection and possibly backupprotection are taken into account (e.g., the switching capacity of a downstreamswitch can be increased as the upstream circuit breaker trips simultaneouslyand, thereby, limits the current)

IEC 60909-0 includes a standard procedure for the calculation of short-circuitcurrents in low-voltage and high-voltage networks up to 550 kV at 50 or 60 Hz [1].The purpose of this procedure is to define a brief, general, and easy-to-handle cal-culation procedure, which is intended to lead with sufficient accuracy to results

on the safe side For this purpose, we calculate with an equivalent voltage source

Fault Current Analysis 27

at the position of the short circuit It is also possible to use the superpositionmethod here

A complete calculation of the time behavior for far-from-generator and to-generator short circuits is not required here In most cases, it is sufficient tocalculate the three-phase and the single-phase short-circuit currents, assumingthat for the duration of the short circuit no change takes place in the type of shortcircuit, the step switch of the variable-ratio transformers is set to the principaltapping and arc resistances can be neglected

near-The short-circuit currents and short-circuit impedances can always be mined by the following methods:

deter-• calculation by hand,

• calculation using a PC,

• using field tests, and

• measurements on network models

The short-circuit currents and short-circuit impedances can be measured inlow-voltage networks by measuring instruments directly at the assumed position

of the short circuit

For the dimensioning and the choice of operational equipment and overcurrentprotective equipment, the calculation of short-circuit currents in three-phasenetworks is of great importance, since the electrical systems must be designednot only for the normal operational state, but also to withstand fault situations.IEC 60909-0 describes the basis for calculation, which consists of the followingparts:

1) Main Part I describes the application areas and the definitions

2) Main Part II explains the characteristics of short circuits and their currentsand the calculation method of equivalent voltage source

3) Main Section III deals with the short-circuit impedances of electrical ment, the impedance correction factors of generators, power transformers,and power stations

equip-4) Main Section IV provides the calculation of the individual short-circuit rents

cur-Summary of IEC 60909-0:

• Restructuring of calculations

• The supplementary pages with examples and conversion factors supplementthe theoretical part

• The high-voltage and low-voltage networks are treated in the same way

• The rules for calculating the smallest and largest short circuits are equally validfor high-voltage and low-voltage networks

• The corrections to the impedances of generators and power plant blocks donot depend on the time behavior of the short-circuit current

• In low-voltage networks, a temperature rise of 20–80 ∘C is assumed for thesingle-phase short circuit This increases the resistance of the cable or con-ductor by a factor of 1.24

• The indices for symmetrical components (0, 1, 2) are internationallystandardized

• The short-circuit currents are determined with the equivalent voltage sourcemethod, in accordance with IEC 60909-0 For this, the internal voltages in thenetwork are short-circuited The only effective voltage at the position of theshort circuit is thenc√⋅Un

3, where c is the voltage factor.

• The superposition method is the more accurate method However, thisrequires the knowledge of the network conditions before the occurrence ofthe short circuit